Peel it, fill it
Show on a big screenOne toy, two questions. How much paint, and how much water?
- One toy, one smooth outline.
- Peel colours the outside only.
- The join is never in that colour.
- Fill takes every bit of space inside.
Area or volume
Paint needs the area of the outside. Water needs the volume inside.
The toy is a cone on a hemisphere. Both have radius 21, and the cone is 28 tall. The cone's slant height is 35. In the formulas, r = 21, h = 28 and l = 35. Also 21 × 21 = 441, and 21 × 21 × 21 = 9261.
Paint covers the outside. That is surface area, in square units. The skin of a cone or dome is its curved surface.
- Cone skin: πrl = 22/7 × 21 × 35 = 2310.
- Dome skin: 2πr² = 2 × 22/7 × 441 = 2772.
- Surface area = 2310 + 2772 = 5082 square units.
Water fills the inside. That is volume, in cubic units.
- Cone: (1/3)πr²h = (1/3) × 22/7 × 441 × 28 = 12936.
- Hemisphere: (2/3)πr³ = (2/3) × 22/7 × 9261 = 19404.
- Volume = 12936 + 19404 = 32340 cubic units.
Words like paint, cloth and polish ask for area. Words like water, air and capacity ask for volume.
Surface area covers the outside, so it counts squares. Volume fills the inside, so it counts cubes. For area, add the outside parts. For volume, add both whole solids.
Tap Paint the outside, then Fill with water.
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Try the lab to finish this lesson.